Prime Factorisation of 420, 468, 945 and 7325

Video Explanation

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Solution

Question: Express each of the following integers as a product of its prime factors:

(i) 420    (ii) 468    (iii) 945    (iv) 7325

(i) Prime Factorisation of 420

420 = 2 × 210
= 2 × 2 × 105
= 2 × 2 × 3 × 35
= 2 × 2 × 3 × 5 × 7

∴ 420 = 2² × 3 × 5 × 7

(ii) Prime Factorisation of 468

468 = 2 × 234
= 2 × 2 × 117
= 2 × 2 × 3 × 39
= 2 × 2 × 3 × 3 × 13

∴ 468 = 2² × 3² × 13

(iii) Prime Factorisation of 945

945 = 3 × 315
= 3 × 3 × 105
= 3 × 3 × 3 × 35
= 3 × 3 × 3 × 5 × 7

∴ 945 = 3³ × 5 × 7

(iv) Prime Factorisation of 7325

7325 = 5 × 1465
= 5 × 5 × 293

∴ 7325 = 5² × 293

Final Answer

420 = 2² × 3 × 5 × 7
468 = 2² × 3² × 13
945 = 3³ × 5 × 7
7325 = 5² × 293

Conclusion

Thus, each of the given integers has been expressed as a product of its prime factors using the method of prime factorisation.